JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    The number of distinct rational numbers x such that \[0<x<1\] and \[x=\frac{p}{q},\] where \[p,q\in \{1,2,3,4,5,6\},\] is

    A) 15

    B) 13

    C) 12

    D) 11

    Correct Answer: D

    Solution :

    [d] As \[0<x<1,\] we have \[p<q\] The number of rational numbers \[=5+4+3+2+1=15.\] When p, q have a common factor, we get some rational numbers which are not different from those already counted. There are 4 such numbers: \[\frac{2}{4},\frac{2}{6},\frac{3}{6},\frac{4}{6}\] Therefore, required number of rational numbers \[=15-4=11.\]

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